Slug-flow true liquid

The Bernoulli equation can now be written for the liquid in channel flow in the bottom part of the tube, and for the liquid in slug flow in the upper part. The acceleration terms are then neglected, and the friction factors for each type of liquid flow found from the Blasius equation and from true Reynolds numbers. The resulting equations cannot be readily evaluated because of the two hydraulic-radius terms involved in the two types of flow, and an unknown fraction defining the relative mass of liquid in each part of the tube. 

Considering a section of a vertical pipe through the base of a gas slug where the liquid film thickness is constant, and calling the gas volume fraction at this point Ro and the true point gas flow Qo, we find from Eq. (46) that... 

It is interesting to compare the assumptions made by Bankoff to the restrictions operating in the investigation by Nicklin, Wilkes, and Davidson for slug flow. In their work the velocity component of the slugs due to liquid flow approached the maximum liquid velocity at the tube center-line. If this is also true of the bubbles of Bankoff s model and the bubble rise velocity due to buoyancy is ignored, then the velocity of the bubbles as given by Nicklin et al. would be,... 

Wallis points out that, from continuity considerations and bubble dynamics, the cocurrent flow of uniformly dispersed bubbles as a discontinuous phase in a liquid can always be made to occur in any system and for any void volume. (This is not true for countercurrent flow.) Coalescence of bubbles may occur, of course, and if this coalescence is sufiiciently rapid, a developing type of flow is observed, usually from bubble to slug flow. Because of this behavior, the particular flow pattern observed in bubble flow is quite dependent on the previous history of the two-phase mixture. This would be true for both horizontal and vertical flow. 

The literature on measurement of mass transfer in vertical tubular reactors is very sparse. Kasturi and Stepanek (K3, K4) have presented data for a, ki a, and kca measured under identical conditions in the case of annular flow, annular spray flow, and slug flow. For the aqueous systems used (COj, air, NaOH) they have proposed the following correlation for the interfacial area fl = 0.23[(l - a)/QJ(AP/Z)i( whereQt is incm /sec and AP/Z is in N/m . Correlations for true liquid-side and gas-side mass-transfer coefficients by the same authors are difficult to generalize, as viscosity and surface tension were not varied. 

This is not true because the slug is found to rise with a velocity 0.35VigDp) relative to the centre-line velocity of the liquid. The liquid flow will be turbulent and its centre-line velocity therefore approximately 20 per cent greater than its average velocity. Thus the correct expression for the slug s velocity is... 

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